62 citations · 279 across the 22 of their papers we have counts for
19 papers · 1 filter
Scaling Symmetry Reductions of Coupled KdV Systems
Allan P Fordy
In this paper we discuss the Painlevé reductions of coupled KdV systems. We start by comparing the procedure with that of {\em stationary reductions}. Indeed, we see that exactly t…
Stationary Coupled KdV Hierarchies and Related Poisson Structures
Allan P. Fordy, Qing Huang
In this paper we continue our analysis of the stationary flows of component, coupled KdV (cKdV) hierarchies and their modifications. We describe the general structure of the $t…
Stationary Flows Revisited
Allan P. Fordy, Qing Huang
In this paper we revisit the subject of stationary flows of Lax hierarchies of a coupled KdV class. We explain the main ideas in the standard KdV case and then consider the dispers…
Integrable and Superintegrable Extensions of the Rational Calogero-Moser Model in 3 Dimensions
Allan P. Fordy, Qing Huang
We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particul…
Adding Potentials to Superintegrable Systems with Symmetry
Allan P. Fordy, Qing Huang
In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamilto…
The Role of Commuting Operators in Quantum Superintegrable Systems
Allan P. Fordy
We discuss the role of commuting operators for quantum superintegrable systems, showing how they are used to build eigenfunctions. These ideas are illustrated in the context of res…
Superintegrable Systems on 3 Dimensional Conformally Flat Spaces
Allan P. Fordy, Qing Huang
We consider Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the conformal algebra to build additiona…
Eisenhart Lift of --Dimensional Mechanics
Allan P. Fordy, Anton Galajinsky
The Eisenhart lift is a variant of geometrization of classical mechanics with degrees of freedom in which the equations of motion are embedded into the geodesic equations of a…
Generalised Darboux-Koenigs Metrics and 3-Dimensional Superintegrable Systems
Allan P. Fordy, Qing Huang
The Darboux-Koenigs metrics in 2D are an important class of conformally flat, non-constant curvature metrics with a single Killing vector and a pair of quadratic Killing tensors. I…
First Integrals from Conformal Symmetries: Darboux-Koenigs Metrics and Beyond
Allan P. Fordy
On spaces of constant curvature, the geodesic equations automatically have higher order integrals, which are just built out of first order integrals, corresponding to the abundance…
A Kaluza-Klein Reduction of Super-integrable Systems
Allan P. Fordy
Given a super-integrable system in degrees of freedom, possessing an integral which is linear in momenta, we use the "Kaluza-Klein construction" in reverse to reduce to a lower…
Classical and Quantum Super-integrability: From Lissajous Figures to Exact Solvability
Allan P. Fordy
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the reson…
Poisson Algebras and 3D Superintegrable Hamiltonian Systems
Allan P. Fordy, Qing Huang
Using a Poisson bracket representation, in 3D, of the Lie algebra , we first use highest weight representations to embed this into larger Lie algebras. These are…
Self-Dual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice
Allan P. Fordy, Pavlos Xenitidis
We recently introduced a class of graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduce…
A note on some superintegrable Hamiltonian systems
Allan P. Fordy
We consider some examples of superintegrable system which were recently isolated through a differential Galois group analysis. The identity of these systems is clarified and the co…
graded discrete Lax pairs and Yang-Baxter maps
Allan P. Fordy, Pavlos Xenitidis
We recently introduced a class of graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper we introduce…
graded discrete Lax pairs and discrete integrable systems
Allan P. Fordy, Pavlos Xenitidis
We introduce a class of graded discrete Lax pairs, with matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs…
Discrete integrable systems and Poisson algebras from cluster maps
Allan Fordy, Andrew Hone
We consider nonlinear recurrences generated from cluster mutations applied to quivers that have the property of being cluster mutation-periodic with period 1. Such quivers were com…
Mutation-Periodic Quivers, Integrable Maps and Associated Poisson Algebras
Allan P Fordy
We consider a class of map, recently derived in the context of cluster mutation. In this paper we start with a brief review of the quiver context, but then move onto a discussion o…